What would searching the Internet provide the models that they don’t already have? Most likely data sources such as stack overflow, documentation on the language it’s targeting, and a variety of relevant forum posts are already part of its training set.

Unless someone else came along and said “here’s how to solve x problem step by step”, I don’t see how additional information past its cutoff point would help. (Perhaps the AI could post on a forum and wait for an answer?)

Yes, iterative programming could help via access to tools- I can see that helping.